Expand Using Sum/Difference Formulas sin(255)

Problem

sin(255)

Solution

1. Identify two angles that sum or subtract to 255 using standard angles from the unit circle. We can use 210 and 45 because 210 + 45 = 255$.

2. Apply the formula for the sine of a sum, which is sin(A+B)=sin(A)*cos(B)+cos(A)*sin(B)

3. Substitute the values A=210 and B=45 into the formula.

sin(210+45)=sin(210)*cos(45)+cos(210)*sin(45)

4. Evaluate the trigonometric functions for the specific angles.

sin(210)=−1/2

cos(45)=√(,2)/2

cos(210)=−√(,3)/2

sin(45)=√(,2)/2

5. Multiply the terms together.

sin(255)=(−1/2)*(√(,2)/2)+(−√(,3)/2)*(√(,2)/2)

sin(255)=−√(,2)/4−√(,6)/4

6. Simplify the expression by combining the fractions over a common denominator.

sin(255)=(−√(,2)−√(,6))/4

Final Answer

sin(255)=(−√(,2)−√(,6))/4

Want more problems? Check here!